MoebiusTom( tom )
MoebiusTom computes the Maccent127 obius values both of the subgroup
lattice of the group with table of marks tom and of the poset of
conjugacy classes of subgroups. It returns a record where the component
mu contains the Maccent127 obius values of the subgroup lattice, and
the component nu contains the Maccent127 obius values of the poset.
Moreover, according to a conjecture of Isaacs et al. (see HIO89,
Pah93), the values on the poset of conjugacy classes are derived
from those of the subgroup lattice. These theoretical values are
returned in the component ex. For that computation, the derived
subgroup must be known in the component derivedSubgroup of tom. The
numbers of those subgroups where the theoretical value does not coincide
with the actual value are returned in the component hyp.
gap> MoebiusTom( a5 );
rec(
mu := [ -60, 4, 2,,, -1, -1, -1, 1 ],
nu := [ -1, 2, 1,,, -1, -1, -1, 1 ],
ex := [ -60, 4, 2,,, -1, -1, -1, 1 ],
hyp := [ ] )
GAP 3.4.4